Hey guys I cant do this following question so thanks in advance if you could help!

A bag contains 2 red marbles, 5 white marbles and 3 black marbles. A game is played with a player randomly drawing one marble at a time from the bag with replacement, continuing until he obtains a red marble or a white marble. He wins if the last marble is white and loses otherwise.

(a) Find the probability that the player wins.
(b) Find the minimum value of n for which P(he draws at most n marble to win) is more than or equal to 0.7.

Apr 27th 2007, 12:10 PM

Soroban

Hello, margaritas!

I can help with part (a) . . . I'm still working on part (b).

Quote:

A bag contains 2 red marbles, 5 white marbles and 3 black marbles. .A game is played
with a player randomly drawing one marble at a time from the bag with replacement,
continuing until he obtains a red marble or a white marble.
He wins if the last marble is white and loses otherwise.

He could win on the second draw.. . He must draw B on the first draw: P(B1) = 0.3. . then draw W on the second draw: P(W2) = 0.5
Hence: .P(W2).= .(0.5)(0.3)

He could win on the third draw.. . He must draw B on the first draw: P(B1) = 0.3. . then draw B on the second draw: P(B2) = 0.3. . then draw W on the third draw: P(W3) = 0.5
Hence: .P(W3) .= .(0.5)(0.3)▓

Hey guys I cant do this following question so thanks in advance if you could help!

A bag contains 2 red marbles, 5 white marbles and 3 black marbles. A game is played with a player randomly drawing one marble at a time from the bag with replacement, continuing until he obtains a red marble or a white marble. He wins if the last marble is white and loses otherwise.

(a) Find the probability that the player wins.
(b) Find the minimum value of n for which P(he draws at most n marble to win) is more than or equal to 0.7.

(a) Since the marbles are replaced after each draw the probability on a given
draw of a play ending in a win is constant, as is the probability of a loss. So of those
games which end on any draw 5/7 are wins and 2/7 are loses. As the game
will eventualy end (with probability 1) 5/7 is the probability that it ended in
a win.

RonL

Apr 28th 2007, 07:49 AM

margaritas

Thanks so much Soroban and CaptainBlack, I understand part (a) now but still cant get part (b) though!

Apr 28th 2007, 08:27 AM

CaptainBlack

Quote:

Originally Posted by margaritas

Hey guys I cant do this following question so thanks in advance if you could help!

A bag contains 2 red marbles, 5 white marbles and 3 black marbles. A game is played with a player randomly drawing one marble at a time from the bag with replacement, continuing until he obtains a red marble or a white marble. He wins if the last marble is white and loses otherwise.

(a) Find the probability that the player wins.
(b) Find the minimum value of n for which P(he draws at most n marble to win) is more than or equal to 0.7.

(b) the probability that the game ends with a win on the r-th draw is:

p(r) = (3/10)^(r-1) (5/10)

That is the game must not finish on the first r-1 draws, and must end
with a win on the r-th draw.

P(he draws at most n marble to win) = sum_{r=1 to n} p(r)

.......= (5/10) [1+(3/10) + (3/10)^2 + ... + (3/10)^{n-1}]

.......= (5/10)[1+(3/10)^{n}]/[1-(3/10)]

Now by trial and error we find P(he draws at most 3 marble to win)~=0.695
and P(he draws at most 4 marble to win)~= 0.7085, so the minimum n such
that P(he draws at most n marble to win)>=0.7 is 4.

(By the way all of this is implicit in Soroban's solution - the main problem that
I had with it was working out what the h*** it was asking)

RonL

Apr 28th 2007, 09:14 AM

Soroban

Hello again, Margaritas!

Quote:

(b) Find the minimum value of n for which:. . .P(he draws at most n marble to win) > 0.7